Patients with severe respiratory illness may require assistance with their breathing if their lungs are stiff, the respiratory muscles weak, or if oxygenation of the blood is inadequate due to lung disease. Respiratory assistance is given by blowing air/oxygen mixtures into the lungs using a mechanical ventilator to expand the lungs and take over some, or all, of the work of breathing.
Patients who are often breathing spontaneously during mechanical ventilation may "fight the ventilator" when they are trying to breathe at different times from the action of the ventilator. This creates problems in the exchange of gases in the lungs, can lead to sudden changes in the action of the heart and in the blood pressure, and can affect the flow of blood to the brain when the patients are severely ill. These adverse effects of "fighting the ventilator" are seen most dramatically in the sick, prematurely born infant. These tiny infants are at risk from brain damage when their breathing patterns become disordered, and more efficient methods of mechanical ventilation are constantly being sought for this group. Rapid changes in clinical state, irritability and the presence of airway reflexes lead to complex and rapidly changing interactions between the baby and the mechanical ventilator. Muscle paralysis is used to suppress spontaneous respiratory efforts, but may be associated with cardiovascular compromise and the need for higher inflating pressures. New techniques of mechanical ventilation attempt to induce and maintain phase-locking or phase-synchrony by the use of fast rates and short inspiratory times, or by triggering ventilator inflation using sensors to detect diaphragmatic excursion. In clinical practice, mechanical ventilation of the newborn is hampered by an inability to assess baby-ventilator interactions by clinical observation at the high spontaneous respiratory frequencies seen (typically 1-2 Hz). Spontaneous respiratory activity is frequently erratic and accompanied by unpredictable activity such as hiccoughs, gasps and responses to painful and other stimuli. An ideal respiratory monitoring system would be able to track the phase, amplitude and frequency of spontaneous respiratory activity relative to mechanical inflation from breath to breath.
The physiological interactions underlying cardiorespiratory control are usually non-linear in nature. Entrainment of biological oscillatory rhythms, such as spontaneous respiratory activity, can be achieved under certain conditions by the application of a periodic stimulus, such as mechanical ventilation, provided that sufficient afferent information reaches the rhythm generator to bring about entrainment. During stable entrainment the output frequency of the spontaneous oscillator will be drawn into simple integer relationships with that of the periodic stimulus, and a fixed phase relationship will be maintained indefinitely, provided stochastic noise is minimal.
In order to achieve an adequate description of the complex changes which characterise the response of stimulated nonlinear systems in physiology we have developed a method (the frequency tracking locus) of tracking cycle-by-cycle changes as opposed to the steady state response. The advantage of the frequency tracking locus method is that it allows a quantitative estimate of the state of entrainment in a stimulated system, as well as providing a visualisation of the interactions between the stimulus and the output from the system.
The frequency response of a linear system may be determined by applying sinusoids of a fixed frequency and calculating the amplitude and phase difference between input and output. The steady-state frequency response of the system can be determined over its entire range by applying input sinusoids incrementally. In nonlinear oscillatory systems the input and output do not exhibit either a fixed amplitude ratio or phase relationship.
A key factor in the analysis of the interaction of nonlinear oscillations is the ability to track frequencies and transients in both stimulus and output signals. Under steady state conditions frequency tracking can be achieved by the use of Fourier estimators, but as entrainment of a nonlinear oscillator becomes unstable, the output oscillation becomes non-stationary. The Fourier integral is based on the assumption that the data extend over an infinite range without any change in frequency content i.e. the waveform is stationary. In practice this condition is never met, but accurate, practical frequency resolution can be achieved with a minimum of approximately 3 to 5 cycles of the fundamental frequency (the lowest frequency in the waveform). Consequently, Fourier estimation has been successful in those biological studies where experimental design has determined the stationarity of the frequency content. Examples of such studies include monitoring thermal entrainment of physiological rhythms, heart rate variability, controlled breathing experiments and observations of the effects of respiration on blood pressure in the newborn. When studies of physiological systems involve the analysis of spontaneous activity, however, it is known that nonlinearities in the control structure induce non-stationarities in the associated waveforms. Hence, Fourier estimators are unable to track the shorter periods of stationarity which occur. In this case we and others have applied linear estimation methods which can resolve over stationary data lengths of 1.5 cycles of the fundamental. While these methods have proved useful, they have two principal disadvantages in relation to the study of nonlinear oscillations. First, a great deal of care must be taken to define parameters such as model order, which can profoundly affect the behaviour of linear estimators. Results from the use of different model orders should be interpreted with extreme caution. Second, transient interactions cannot be defined by this approach. Unstable states of entrainment are characterised by significant non-stationarity in the response of a system, during which relationships change from cycle to cycle and even autoregressive spectral estimation will fail. The frequency tracking locus (as described below) is specifically designed for these conditions and can give cycle by cycle descriptions of the phase-amplitude parameter space and its variation with time.
The rhythmical neuronal activity responsible for spontaneous respiratory drive and the effects upon it of periodic lung inflations have been modelled using forced, non-linear equations. Where patients are allowed to breathe spontaneously during mechanical ventilation, such as in the sick newborn infant, stable entrainment is difficult to achieve. Studies of interactions between spontaneous respiratory activity and mechanical ventilators in adult humans and in animal models have revealed that entrainment of spontaneous respiration by the ventilator stimulus can occur under favourable conditions. In adults and animals entrainment appears to be induced by the activity of reflexes: the Hering-Breuer inflation reflex (which shortens spontaneous inspiration when inflation occurs during inspiration) and the Hering-Breuer deflation reflex (which lengthens expiration when inflation occurs during spontaneous expiration). Vagotomy abolishes entrainment, demonstrating the essential role of pulmonary reflexes mediated by parasympathetic pathways. Respiratory reflexes similar to those inducing entrainment in adults are present in the neonate.